Abstract

where m and n are positive integers, in terms of the Riemann zeta
function. In [Borwein et al.\ 1993], Euler's results were extended to
a significantly larger class of sums of this type, including sums with
alternating signs.

This research was facilitated by numerical computations using an
algorithm that can determine, with high confidence, whether or not a
particular numerical value can be expressed as a rational linear
combination of several given constants. The present paper presents
the numerical techniques used in these computations and lists many of
the experimental results that have been obtained.